def test_constant_offset(self):
offset_ = 1.23456
offset = self._build_placeholder(offset_)
ssm = self._dummy_model()
additive_ssm = AdditiveStateSpaceModel([ssm])
additive_ssm_with_offset = AdditiveStateSpaceModel(
[ssm], constant_offset=offset)
additive_ssm_with_offset_and_explicit_scale = AdditiveStateSpaceModel(
[ssm],
constant_offset=offset,
observation_noise_scale=(
ssm.get_observation_noise_for_timestep(0).stddev()[..., 0]))
mean_, offset_mean_, offset_with_scale_mean_ = self.evaluate(
(additive_ssm.mean(), additive_ssm_with_offset.mean(),
additive_ssm_with_offset_and_explicit_scale.mean()))
print(mean_.shape, offset_mean_.shape, offset_with_scale_mean_.shape)
self.assertAllClose(mean_, offset_mean_ - offset_)
self.assertAllClose(mean_, offset_with_scale_mean_ - offset_)
# Offset should not affect the stddev.
stddev_, offset_stddev_, offset_with_scale_stddev_ = self.evaluate(
(additive_ssm.stddev(), additive_ssm_with_offset.stddev(),
additive_ssm_with_offset_and_explicit_scale.stddev()))
self.assertAllClose(stddev_, offset_stddev_)
self.assertAllClose(stddev_, offset_with_scale_stddev_)
def test_nesting_additive_ssms(self):
ssm1 = self._dummy_model(batch_shape=[1, 2])
ssm2 = self._dummy_model(batch_shape=[3, 2])
observation_noise_scale = 0.1
additive_ssm = AdditiveStateSpaceModel(
[ssm1, ssm2], observation_noise_scale=observation_noise_scale)
nested_additive_ssm = AdditiveStateSpaceModel(
[AdditiveStateSpaceModel([ssm1]),
AdditiveStateSpaceModel([ssm2])],
observation_noise_scale=observation_noise_scale)
# Test that both models behave equivalently.
y = self.evaluate(nested_additive_ssm.sample())
additive_lp = additive_ssm.log_prob(y)
nested_additive_lp = nested_additive_ssm.log_prob(y)
self.assertAllClose(self.evaluate(additive_lp),
self.evaluate(nested_additive_lp))
additive_mean = additive_ssm.mean()
nested_additive_mean = nested_additive_ssm.mean()
self.assertAllClose(self.evaluate(additive_mean),
self.evaluate(nested_additive_mean))
additive_variance = additive_ssm.variance()
nested_additive_variance = nested_additive_ssm.variance()
self.assertAllClose(self.evaluate(additive_variance),
self.evaluate(nested_additive_variance))
def test_constant_offset(self, is_scalar=True):
offset_ = np.array(3.1415) if is_scalar else np.array(
[3., 1., 4., 1., 5.])
offset = self._build_placeholder(offset_)
ssm = self._dummy_model()
additive_ssm = AdditiveStateSpaceModel([ssm])
additive_ssm_with_offset = AdditiveStateSpaceModel(
[ssm], constant_offset=offset)
additive_ssm_with_offset_and_explicit_scale = AdditiveStateSpaceModel(
[ssm],
constant_offset=offset,
observation_noise_scale=(
ssm.get_observation_noise_for_timestep(0).stddev()[..., 0]))
mean_, offset_mean_, offset_with_scale_mean_ = self.evaluate(
(additive_ssm.mean(), additive_ssm_with_offset.mean(),
additive_ssm_with_offset_and_explicit_scale.mean()))
self.assertAllClose(mean_, offset_mean_ - offset_[..., tf.newaxis])
self.assertAllClose(mean_,
offset_with_scale_mean_ - offset_[..., tf.newaxis])
# Offset should not affect the stddev.
stddev_, offset_stddev_, offset_with_scale_stddev_ = self.evaluate(
(additive_ssm.stddev(), additive_ssm_with_offset.stddev(),
additive_ssm_with_offset_and_explicit_scale.stddev()))
self.assertAllClose(stddev_, offset_stddev_)
self.assertAllClose(stddev_, offset_with_scale_stddev_)
def test_sum_of_local_linear_trends(self):
# We know analytically that the sum of two local linear trends is
# another local linear trend, with means and variances scaled
# accordingly, so the additive model should match this behavior.
level_scale = 0.5
slope_scale = 1.1
initial_level = 3.
initial_slope = -2.
observation_noise_scale = 0.
num_timesteps = 5
y = self._build_placeholder([1.0, 2.5, 4.3, 6.1, 7.8])
# Combine two local linear trend models, one a full model, the other
# with just a moving mean (zero slope).
local_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=level_scale,
slope_scale=slope_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder([initial_level, initial_slope]),
scale_diag=self._build_placeholder([1., 1.])))
second_level_scale = 0.3
second_initial_level = 1.1
moving_level_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=second_level_scale,
slope_scale=0.,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder([second_initial_level, 0.]),
scale_diag=self._build_placeholder([1., 0.])))
additive_ssm = AdditiveStateSpaceModel(
[local_ssm, moving_level_ssm],
observation_noise_scale=observation_noise_scale)
# Build the analytical sum of the two processes.
target_ssm = LocalLinearTrendStateSpaceModel(
num_timesteps=num_timesteps,
level_scale=np.float32(
np.sqrt(level_scale**2 + second_level_scale**2)),
slope_scale=np.float32(slope_scale),
observation_noise_scale=observation_noise_scale,
initial_state_prior=tfd.MultivariateNormalDiag(
loc=self._build_placeholder(
[initial_level + second_initial_level,
initial_slope + 0.]),
scale_diag=self._build_placeholder(np.sqrt([2., 1.]))))
# Test that both models behave equivalently.
additive_mean = additive_ssm.mean()
target_mean = target_ssm.mean()
self.assertAllClose(self.evaluate(additive_mean),
self.evaluate(target_mean))
additive_variance = additive_ssm.variance()
target_variance = target_ssm.variance()
self.assertAllClose(self.evaluate(additive_variance),
self.evaluate(target_variance))
additive_lp = additive_ssm.log_prob(y[:, np.newaxis])
target_lp = target_ssm.log_prob(y[:, np.newaxis])
self.assertAllClose(self.evaluate(additive_lp),
self.evaluate(target_lp))
